Stability of topological edge states in nonlinear quantum walks: Bifurcations unique to Floquet systems

Quantum walk, which is a kind of Floquet systems where time evolves in a discrete manner, can possess nontrivial topological phases. Recently, quantum walks with nonlinear effects have been proposed theoretically. Taking these features into account, we study the stability of topologically protected edge states in nonlinear quantum walks. In contrast to the previous work [1] which ignores the discrete-time nature, we analyze the stability taking the discreteness of time into account [2]. As a result, we find a new bifurcation where edge states change from stable attractors to unstable repellers. The bifurcation is unique to Floquet systems since it originates from the discreteness of time. Furthermore, because of the simpleness of the quantum walk, we analytically derive the bifurcation thresholds, which are generally difficult to obtain in a wide range of nonlinear systems.

[1] Y. Gerasimenko, B. Tarasinski, and C.W. J. Beenakker, Phys. Rev. A 93, 022329 (2016).
[2] K. Mochizuki, N. Kawakami, and H. Obuse, Journal of Physics A 53, 085702 (2020).